A Decomposition Method for Computing System Reliability by a Boolean Expression

A substitutionary decomposition method for computing the reliability of a redundant system S given by a Boolean expression is proposed, System S is decomposed into two subsystems S(x) and S(x?) according to up-and down-states of its keystone variable x. This is repeated until all terms become s-independent in each decomposed subsystem. A criterion for choosing the keystone variable and a property which saves computation time are obtained.